The present invention relates to a new and distinct cultivar of Nepeta named ‘Kitten Around’. The new plant resulted from a cross between Nepeta ‘Purrsian Blue’ U.S. Plant Pat. No. 24,788 as the female or seed parent and Nepeta ‘Psfike’ U.S. Plant Pat. No. 18,904 as the male or pollen parent directed by the inventor on Jun. 12, 2012. Seed was harvested Aug. 7, 2012 and eventually assigned the breeder code 12-2-2 toward the end of the trial period. ‘Kitten Around’ was approved in a final evaluation in the summer of 2015 and slated for later introduction. The new plant was selected based on the compact habit and repeat blooming following trimming. The new plant has been asexually propagated by tip cuttings with the resultant plants remaining identical to the original plant, stable and true to type in successive generations.